Cohomology of Vector Bundles and Syzygies [Hardcover]

An exposition of the important geometric technique of calculating syzygies.The central theme of this book is a detailed exposition of the geometric technique of calculating syzygies. While this is an important tool in algebraic geometry the author has elected to write from the point of view of commutative algebra in order to avoid being tied to special cases from geometry. No prior knowledge of representation theory is assumed. Chapters on several applications are included, and numerous exercises will give the reader insight into how to apply this important method.The central theme of this book is a detailed exposition of the geometric technique of calculating syzygies. While this is an important tool in algebraic geometry the author has elected to write from the point of view of commutative algebra in order to avoid being tied to special cases from geometry. No prior knowledge of representation theory is assumed. Chapters on several applications are included, and numerous exercises will give the reader insight into how to apply this important method.The central theme of this book is a detailed exposition of the geometric technique of calculating syzygies. While this is an important tool in algebraic geometry, Jerzy Weyman has elected to write from the point of view of commutative algebra in order to avoid being tied to special cases from geometry. No prior knowledge of representation theory is assumed. Chapters on several applications are included, and numerous exercises will give the reader insight into how to apply this important method.1. Introduction; 2. Schur functions and Schur complexes; 3. Grassmannians and flag varieties; 4. Bott's theorem; 5. The geometric technique; 6. The determinantal varieties; 7. Higher rank varieties; 8. The nilpotent orbit closures; 9. Resultants and discriminants....it is a useful reference, in particular for those advanced undergraduates and graduate university students who are considering the development of their knowledge in hils¢